The factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.
A quadratic expression is of the form ax² + bx + c, which can be factorized using the mid-term factorization method, where b is shown as the sum or difference of two such numbers, whose product is equal to the product of a and c.
In the question, we are asked to factorize the quadratic expression, x² - 4x - 21.
In the given expression, a = 1, b = -4, and c = -21.
Thus, ac = -21.
The numbers having a product 21 are:
1*21 = 21,
3*7 = 21.
Since, 3 - 7 = -4 (That is b), we break b into 3 and -7.
Thus, the expression can now be shown as:
x² - 4x - 21
= x² + (3 - 7)x - 21
= x² + 3x - 7x - 21
= x(x + 3) - 7(x + 3) {By taking common}
= (x - 7)(x + 3) {By taking common}.
Thus, the factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.
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Find the equation of a line that is perpendicular to line g that contains (p, q). coordinate plane with line g that passes through the points negative 2 comma 6 and negative 3 comma 2 4x y = q 4p x − 4y = −4q p −4x y = q − 4p x 4y = 4q p
The equation of a line that exists perpendicular to line g contains (P, Q) exists x + 4y = 4Q + P.
How to estimate the equation of the line that exists perpendicular to line g that contains (p, q) coordinate plane with line g?
Given: Coordinate plane with line g that passes through the points (-2,6) and (-3,2).
The coordinate of G: (-2,6) and (-3,2)
Let, [tex]$&\left(x_{1}, y_{1}\right)=(-2,6) \\[/tex] and [tex]$&\left(x_{2}, y_{2}\right)=(-3,2)[/tex]
The slope of a line [tex]$\mathbf{g}$[/tex] :
[tex]$m &=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\[/tex]
[tex]$m &=\frac{2-6}{-3-(-2)} \\[/tex]
[tex]$m &=\frac{-4}{-1} \\[/tex]
m = 4
So, the slope of a line g exists 4.
To find the slope of a line perpendicular to g,
[tex]$&m_{1}=-\frac{1}{m} \\[/tex]
[tex]$&m_{1}=-\frac{1}{4}[/tex]
The equation of the slope point form of the line exists
[tex]$\left(y-y_{1}\right)=m\left(x-x_{1}\right)$[/tex]
[tex]$y-Q=-\frac{1}{4}(x-P)$[/tex]
[tex]$4 y-4 Q=-x+P$[/tex]
[tex]$x+4 y=4 Q+P$[/tex]
Therefore, the equation of a line that exists perpendicular to line g contains (P, Q) exists x + 4y = 4Q + P.
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At noon, ship a is 40 nautical miles due west of ship b. ship a is sailing west at 18 knots and ship b is sailing north at 17 knots. how fast (in knots) is the distance between the ships changing at 5 pm? (note: 1 knot is a speed of 1 nautical mile per hour.)
The distance between the ships changing at 92.29 Knots
Using the position of ship A as the reference point, at time t measured in hours past noon, ship A is 18 t miles west of this point and ship B is 40 + 17t north of this point. The distance between ships is then[tex]d(t) = \sqrt{(18t)^{2} + (40+17t)^{2} } \\[/tex]
The rate of change of distance is -
[tex]\frac{dd}{dt} = \frac{36t + 2(40 + 17t)17}{2\sqrt{18t^{2} + (40 + 17t) } }[/tex]
after putting t = 5 into this rate of change ,
we get, answer = 92.29
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A juggler is performing her act using several balls. she throws the balls up at an initial height of 4 feet, with a speed of 15 feet per second. this can be represented by the function h(t) = −16t2 15t 4. if the juggler doesn't catch one of the balls, about how long does it take the ball to hit the floor? 7.52 seconds 1.15 seconds 0.47 seconds 0.22 seconds
The ball will take 1.15 seconds to hit the floor.
It is given that,
A juggler is performing her act using several balls. The height as a function of time is given by :
[tex]h(t) =-16t^{2} + vt +s[/tex].............(1)
where,
v is the speed of the ball
s is initial height
t is time taken
Putting h(t) = 0 and solving equation (1)
[tex]-16t^{2} + vt +s = 0[/tex]
[tex]-16t^{2} + 15t +4 = 0[/tex]
On solving above equation using graphing calculator and solving for t we get, t = 1.154 second.
Hence, the correct option is (b) " 1.15 seconds ".
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What is the solution to the system of equations?
[tex](\frac{3}{2},\frac{5}{2})[/tex]
Step-by-step explanation:The first equation can be rearranged by subtracting y from both sides. This gives you x = 4 - y.
The second equation is x = y - 1
Therefore, as both equations are equal to x, you can say that they are equal to each other, so 4 - y = y - 1.
If you add 1 to each side, you get 5 - y = y
If you add y to each side, you get 5 = 2y
Divide both sides by 2 to get y = 5/2
Now you can substitute 5/2 for y. For example, the second equation becomes x = 5/2 - 1
x is therefore 3/2
This can be written as [tex](\frac{3}{2},\frac{5}{2})[/tex], which is the final answer.
PLS HELP ASAP??!! Pls help me with 7,8,8
Answer:
Step-by-step explanation:
1144
Determine what type of model best fits the given situation: water leaking from a local reservior at the rate of 500 gallons per hour.
The type of model that best fits the given situation is; A linear equation Model
What is the model of the equation?Right inside the local reservoir we will have an initial amount of water A.
Now, for every hour that passes by, the amount of water in the reservoir decreases by 500 gals.
Thus, after t hours, the amount of water in the reservoir is expressed as:
W = A - 500gal * t
This is clearly a linear equation model and so we can conclude that the model that fits best in the given situation is a linear model.
The domain of this model is restricted because we can't have a negative amount of water in the reservoir, and as such the maximum value of t accepted is: W = 0 = A - 500gal*t
t = A/500 hours
Therefore, the domain of this linear relation is: t ∈ {0h, A/500 }
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Help!!!!
A system of inequalities is shown.
Which system Is represented in the graph?
The system of inequalities represented on the graph is:
y > 2x + 3.y > (x + 1)² - 4.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The linear function in this problem has y-intercept of b = 3, and also goes through the point (1,5), hence the slope is of 2. The line is dashed, hence it is not included in the solution, hence only the part greater than the line is, hence:
y > 2x + 3
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
In this graph, the vertex of the parabola is of (-1,-4), hence h = -1, k = -4, and the equation is:
y = a(x + 1)² - 4
When x = 0, y = -3, hence the leading coefficient is found as follows:
-3 = a - 4
a = 1.
Hence:
y = (x + 1)² - 4.
And the inequality is:
y > (x + 1)² - 4.
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rounding to 1 significant figure, estimate the
answers to these questions:
a)
78 × 92
b)
615 × 38
C)
423 × 764
Answer:
a) 7000
b) 20000
c) 300000
Rounding is the act of replacing a number with values that are an approximation.
can be used to create simpler, or more explicit answersBasic rounding rules:
1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. Example: 68 rounded to 1 significant figure would be 70.
2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down. Example: 13 rounded to 1 significant fugue is 10.
3. Zero digits that come after a non zero digit are non significant. Example: 10000 only has 1 significant figure
Calculations:
A) 78 x 92 = 7176
to round to 1 sig fig we must make all digits after 7 insignificantwe must also take note of whether the 7 will remain the same or be rounded upthe digit that comes after is a 1, following the rules of rounding it will remain a 7The answer for A is 7000
B) 615 x 38 = 23370
all digits after 2 must be insignificant the digit that comes after is a 3, following the rules of rounding the 2 will remain a 2Answer for B is 20000
C) 423 x 764 = 323172
all digits after 3 must be insignificantthe digit that comes after is a 2, following the rules of rounding the 3 will remain a 3Answer for C is 300000
Salah is building a brick walkway around his garden, which is 17 feet wide and 40 feet long. he wants the walkway to be 18 inches wide on all sides. if the bricks are 6 inches wide and 8 inches long, what is the minimum number of bricks Salah will have to buy?
The minimum number of bricks Salah will have to buy is 4050 bricks
How to find the minimum number of bricks Salah will have to buy?
Given that the
width of the garden is w = 17 feet and length l = 40 feet. Also, the walkway iis 18 feet wide.So, the length of walkway plus garden, L = 40 ft + 18 ft = 58 ft. The width of walkway plus garden, W = 17 ft + 18 ft = 35 ft.
The area of the walkwayWe now need to find the area of the walkway.
Area of walkway, A" = area of walkway plus garden - area of garden
= LW - lw
= 58 ft × 35 ft - 40 ft × 17 ft
= 2030 ft² - 680 ft²
= 1350 ft²
Now, since each brick is 6 inches wide and 8 inches long, the area of each brick is A' = 6 in × 8 in = 48 in²
So, the number of bricks required, n = area of walkway/area of brick
= 1350 ft²/48 in²
= 1350 × 144 in²/48 in²
= 194400 in²/48 in²
= 4050 bricks
So, the minimum number of bricks Salah will have to buy is 4050 bricks
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What is the answer of the fractions 9 and 1/6 multiplied by 1 and 1/11? Then, that answer simplified into simplest form?
The simplest form is 10.
We can find simplest as form:
Given, fractions are [tex]9\frac{1}{6}[/tex] and [tex]1\frac{1}{11}[/tex]
[tex]9\frac{1}{6}\times 1\frac{1}{11}[/tex]
[tex]\frac{55}{6}\times \frac{12}{11}[/tex]
[tex]=\frac{55\times 12}{6\times 11}[/tex]
=10
Hence, simplest form of given fraction is 10.
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A polygon ABCD is inscribed in a circle. Find m angle D A B.
Answer: [tex]\Large\boxed{\angle DAB=62^\circ}[/tex]
Concept:
Here, we need to know about the idea of a cyclic quadrilateral.
In a cyclic quadrilateral, the sum of either pair of opposite angles is supplementary, which means they add up to 180°.
Please refer to the attachment below for a graphical explanation
Solve:
Given information
∠DAB = 2x + 4
∠ABC = 4y + 4
∠BCD = 4x + 2
∠CDA = 3y + 8
Derived formula from the concept
∠DAB + ∠BCD = 180°
∠ABC + ∠CDA = 180° (Not Important)
Substitute values into the formula that includes ∠DAB
∠DAB + ∠BCD = 180°
(2x + 4) + (4x + 2) = 180
Combine like terms
2x + 4 + 4x + 2 = 180
2x + 4x + 4 + 2 = 180
6x + 6 = 180
Subtract 6 on both sides
6x + 6 - 6 = 180 - 6
6x = 174
Divide 6 on both sides
6x / 6 = 174 / 6
x = 29
Substitute values into the angle expression of ∠DAB
∠DAB = 2x + 4
∠DAB = 2 (29) + 4
∠DAB = 58 + 4
[tex]\Large\boxed{\angle DAB=62^\circ}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Which steps could be part of the process in algebraically solving the system of equations, y 5x = x2 10 and y = 4x – 10? select two options.
The step that is the part of the process of algebraically solving the given system of equations is (C) 4x – 10 = x2 – 5x + 10 and (E) 0 = x2 – 9x + 20.
What is an equation?An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =.To find the step that is the part of the process of algebraically solving the given system of equations:
That would be:
(C) 4x – 10 = x2 – 5x + 10 ( y = 4x - 10 is substituted for y).
Proof:
y + 5x = x² + 10(4x - 10) + 5x = x² + 104x - 10 = x² -5x + 10(E) 0 = x2 – 9x + 20 (liked terms are grouped and simplified).
Proof:
4x - 10 = x² -5x + 104x = x² -5x + 10 + 100 = x² -5x -4x + 200 = x² - 9x + 20Solving:
x² - 9x + 20 = 0 x² - 5x - 4x + 20 = 0(x - 5) (x - 4) = 0x = 4 (as question says) OR x = 5Therefore, the step that is part of the process of algebraically solving the given system of equations is (C) 4x – 10 = x2 – 5x + 10.
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The complete question is given below:
Which steps could be part of the process in algebraically solving the system of equations, y + 5x = x2 + 10 and y = 4x – 10? Check all that apply.
(A) y = x2 + 5x + 10
(B) y + 5x = x2 + 10 + 4x – 10
(C) 4x – 10 = x2 – 5x + 10
(D) 0 = x2 – 9x
(E) 0 = x2 – 9x + 20
(F) One x-value of a solution to the system is 4.
Each sales associate at an electronics store has a choice of the two salary options shown below:
$115 per week plus 9.5% commission on the associate’s total sales
$450 per week with no commission
The average of the total sales amount for each associate last year was $125,000. Based on this average, what is the difference between the two salary options each year? (1 year = 52 weeks)
Using proportions, it is found that the difference between the two salary options each year is of $5,545.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
For the first option, $115 per week plus 9.5% commission on the associate’s total sales, the yearly salary is:
115 x 52 + 0.095 x 125000 = $17,855.
For the second option, $450 per week with no commission, the yearly salary is:
450 x 52 = $23,400.
Hence the difference is given as follows:
23400 - 17855 = $5,545.
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The variable used to predict another variable in a regression analysis (usually x) is called the?
The variable used to predict another variable in a regression analysis (usually x) is called the independent variable.
The regression analysis is used to determine the effect on the dependent variable with every one unit change in the independent variable.
The dependent variable is also known as response.
and the independent variable is also known as predictor.
In case of simple linear regression there is only one independent variable and in cases of multiple linear regression there are more than one independent variables.
The general form of simple linear regression is:
[tex]y=mx+c[/tex]
The general form of multiple linear regression is:
[tex]y=c+m_1x_1+m_2x_2+...+m_nx_n[/tex]
The dependent variable are usually denoted by the letter "y" and the independent variables are usually denoted by the letter "x".
Therefore, the variable used to predict another variable in a regression analysis (usually x) is called the independent variable.
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Match each scenario with the type of correlation it shows.
the time spent practicing and the
number of free throws made
the number of items bought and the
checking account balance
the height of baseball player and the
number of hits made.
000
negative correlation
no correlation
positive correlation
The time spent practicing and the number of free throws made has a positive correlation. The number of items bought and the checking account balance has a negative correlation. The height of baseball player and the
number of hits made has no correlation.
About positive correlation:
Two variables that move together, or in the same direction, are said to have a positive correlation. When one variable rises while the other rises or when one variable falls while the other falls, there is a positive correlation.
About negative correlation:
A negative or inverse relationship between two variables in statistics exists when higher values of one variable tend to be correlated with lower values of the other. Such scenarios have negative correlation.
About no correlation:
When two events or variables are unaffected by each other or are not inter-related, they are said to possess no correlation.
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Answer:
option 1 is positive option 2 is negative option 3 is none
Step-by-step explanation:
Enginuity said so
If BD = 16 yd and the area of rhombus ABCD is 72 yd^2, what is AC?
Formula for finding area of rhombus: [tex]\frac{d1 * d2}{2}[/tex]
d₁ = 16 yd
Area = 72 yd²
Rhombus Area =>
[tex]\frac{16 * d2}{2} = 72[/tex]
16*d₂ = 144
d₂ = 9
AC = 9 yd
Hope it helps!
Given MTS and SQP, find sq
The measure of the side SQ from the given diagram is 19/6
Similar shapesSimilar shapes are shapes that has equal length and equal side measures and angles.
From the given diagram, the measure of the sides TSis congruent to SP and the measure of MS is congruent to SQ.
Using the expression below to determine the value of x
MS/ST = SQ/SP
Given the following parameters
MS =30
ST = 10
SQ = 6x-1
SP = 3 - 2x
Substitute the given parameters into the formula to have:
30/10 = 6x-1/3-2x
Cross multiply
10(6x-1) = 30(3-2x)
Expand
60x - 10 = 90 - 60x
60x + 60x = 90 + 10
120x = 100
x = 10/12
x = 5/6
Determine the measure of SQ
SQ = 6x - 1
SQ = 5(5/6) - 1
SQ = 25/6 - 1
SQ = 19/6
Hence the measure of the side SQ from the given diagram is 19/6
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A school administrator believes that the mean class gpas for a given course are higher than the preferred mean of 2.75 at a significance level of 0.05 , and checks a randomly chosen sample of 50 classes. create a histogram, and calculate , the -statistic, and the -value.
The mean GPA is greater than 2.75.
What is GPA?A grade point average is a figure that represents the average of the final grades obtained in courses over time. A student's grade point average, sometimes known as a GPA, is computed by adding all accumulated final grades and dividing the total by the number of grades granted.To find the GPA:
GPA is calculated and could be utilized by the college to tell choices, which include the subsequent educational progression.Divide the total range of grade factors earned with the aid of the total number of letter-graded units undertaken.Mean GPA = total/50= 2.75.Therefore, the mean GPA is greater than 2.75.
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What is the solution to this system of equations?
4x + 5y = 7
3x – 2y = –12
The solution is
The solution to the system of equations is (-2, 3)
Evaluate the expression under the given conditions. tan(2); cos() = 5 13 , in quadrant i
The solution to given expression tan(2θ) is 22.615°
For given question,
We have been given an expression tan(2θ)
Given that cos(θ) = 5/13, and θ is in quadrant 1.
We know that the trigonometric identity
sin²θ + cos²θ = 1
⇒ cos²θ = (5/13)²
⇒ sin²θ = 1 - 25/169
⇒ sin²θ = 169 - (25/169)
⇒ sin²θ = 144/169
⇒ sin(θ) = 12/13
We know that the identity cos(2x) = cos²x - sin²x
⇒ cos(2θ) = cos²θ - sin²θ
⇒ cos(2θ) = 25/169 - 144/169
⇒ cos(2θ) = -119/169
And sin(2x) = 2sin(x)cos(x)
⇒ sin(2θ) = 2sin(θ)cos(θ)
⇒ sin(2θ) = 2 × 12/13 × 5/13
⇒ sin(2θ) = 120/169
We know that, tan(x) = sin(x)/cos(x)
⇒ tan(2θ) = sin(2θ)/cos(2θ)
⇒ tan(2θ) = (120/169) / (-119/169)
⇒ tan(2θ) = 120 / (-119)
⇒ tan(2θ) = -1.008
Since θ is in quadrant 1, tan(2θ) = 1.008
⇒ 2θ = arctan(1.008)
⇒ 2θ = 45.23
⇒ θ = 22.615°
Therefore, the solution to given expression tan(2θ) is 22.615°
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plsssss help w math functions
Answer:
The second option:
[tex]2\sqrt{x}[/tex]
Step-by-step explanation:
If you need work please ask!
Have a nice day!
the value of digit 7 in 906.7
The answer is tenths
Step-by-step explanation:
According to the place value chart of decimals,the first number after the decimal point starts from tenths and continues.so the answer is tenths
Hi :)
Remember Place value in decimal numbers
———————————[tex]\large\boldsymbol{\hfill\stackrel{hundreds}{9}~\hfill\stackrel{tenths}0~\hfill\stackrel{ones}6.\hfill\stackrel{tenths}{7}}[/tex]
Then
The place-value of [tex]\boldsymbol{7}[/tex] is [tex]\boldsymbol{tenths}[/tex].
[tex]\tt{Learn~More;Work~Harder}[/tex]
:)
The probability distribution histogram shows the age distribution of giraffes at a zoo.
What is P(4
Enter your answer, as a decimal, in the box.
The value of P(4<X≤12) is 0.45
How to determine the probability?The complete question is added as an attachment
To calculate P(4<X≤12), we use the following equation
P(4<X≤12) = P(4<X≤8) + P(8<X≤12)
From the histogram, we have:
P(4<X≤8) = 0.1
P(8<X≤12) = 0.35
So, we have:
P(4<X≤12) = 0.1 + 0.35
Evaluate
P(4<X≤12) = 0.45
Hence, the value of P(4<X≤12) is 0.45
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What are the coordinates of point J'? (-2,-4) (-2,-6) (Negative nine-halves, negative 4) (Negative nine-halves, negative 9)
The coordinates of point J' in the quadrilateral F'G'H'J' is J'(-2, -4)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation.
Quadrilateral FGHJ is dilated according to the rule Do,Two-thirds(x,y) to create the image quadrilateral F'G'H'J', which is not shown. Quadrilateral FGHJ has points F(-5, -4), G(-3, -2), H(-1, -4) and J(-3, -6).
The coordinates of point J' in the quadrilateral F'G'H'J' is J'(-2, -4)
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Answer:
(-2,-4)
Step-by-step explanation:
Geometry B E2020!! :3
When measuring variables, it is often preferable to use a small sample size because:______.
When measuring variables, it is often preferable to use a small sample size because the smaller the sample the greater the chance of a spurious result.
What are variables?A variable is defined as any property, number, or amount that can be measured or counted. A variable is also known as a data item. Variables include age, business revenue and expenses, country of birth, capital expenditure, class grades, eye color, and vehicle type. A variable in research is essentially a person, place, object, or phenomenon that you are attempting to quantify in some way. The simplest way to comprehend the distinction between a dependent and independent variable is to consider what the words tell us about the variable in question. When measuring variables, small sample size is frequently preferred because the smaller the sample, the greater the likelihood of a misleading result.Therefore, when measuring variables, it is often preferable to use a small sample size because the smaller the sample the greater the chance of a spurious result.
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The area of a painting is 4081 c m squared.
If the width of the painting is 53 cm, what is its length, in centimeters?
Type your numerical answer below (without units). If necessary, round to the nearest integer.
Answer:
49,2
Step-by-step explanation:
i dont practice math in english so the variables might be a little different!! The little L with the squiggly is supposed to represent length
The length of the painting is 77 cm if the area of the painting is 4081 sq cm and the width is 53 cm.
The area of a rectangle is the product of the length and width of the same rectangle.
Given that:
The area of the painting, A = 4081 cm².
The width of the painting, b = 53 cm.
To find the length of the painting, use the following formula to obtain the area of the rectangle:
Area = length × breadth
Let the length of the painting is l, then
A = l × b
4081 = l × 53
l = [tex]\frac{4081}{53}[/tex]
l = 77
Thus, the length of the painting is 77 cm.
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(6+q)-xy pllease help this question turn in words
In words (6 + q) - xy is six added to a number subtracted from the product of two numbers
The problem is a algebraic expression
What is an algebraic expression?A algebraic expression a mathematical expression containing one or more variables used to express a word problem
We want to convert the algebraic expression (6 + q) - xy into a word problem.
First, we have 6 + q which is six added to a number.Next, we have xy which is the product of two numbersSince (6 + q) is subtracted from xy, we have (6 + q) - xy as six added to a number subtracted from the product of two numbersSo, (6 + q) - xy in words is six added to a number subtracted from the product of two numbers
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If two marbles are selected at random with replacing between draws, what is the probability that the outcome is red then yellow? (round your answer to four decimal places. )
The probability that the outcome is red then yellow is 0.036.
Given that in a jar there are 8 red marbles, 1 yellow marble and 6 green marbles.
We are required to find the probability of obtaining a red then yelow marble if two marbles are drawn and replacement is used.
Probability is the calculation of finding the chance of happening a event among all the events possible. It lies between 0 and 1.
Probability=Number of items/ Total items.
Number of red marbles=8
Number of yellow marble=1
Number of green marbles=6
Total marbles=15
Probability of obtaining red marble=8/15
Probability of obtaining yellow marble=1/15 (Because replacing is there so the number of total marbles do not decrease)
Required probability=8/15*1/15
=8/225
=0.035555
After rounding off we will get 0.036.
Hence the probability that the outcome is red then yellow is 0.036.
Question is incomplete. The following line should be included in question:
A jar contains 8 red marbles , a yellow marble and 6 green marbles.
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Which shows the following expression after the negative exponents have been eliminated?
Answer:
[tex]\frac{a^3b^4}{ab^2}[/tex] which is the last choice in the question
Step-by-step explanation:
Simplify
[tex]\frac{a^3b^{-2}}{ab^{-4}} = \frac{a^3}{a}\frac{b^{-2}}{b^{-4}}[/tex]
Using the fact that [tex]\frac{x^m}{x^n} =x^{m-n}[/tex]
We get
[tex]\frac{a^3}{a} = a^{3-1} = a^2[/tex]
[tex]\frac{b^{-2}}{b^{-4}} = b^{-2-(-4)} = b^2[/tex]
So
[tex]\frac{a^3b^{-2}}{ab^{-4}} =a^2b^2[/tex]
Multiplying numerator and denominator by [tex]ab^2[/tex] gives
[tex]a^2b^2 \frac{ab^2}{ab^2}[/tex]
= [tex]\frac{a^3b^4}{ab^2}[/tex] ANSWER
Hint:
We can eliminate first choice since negative exponents still remain
We can eliminate third choice because the expression has a minus sign which is not possible
That just leaves second and fourth choices to work with
The numbers of questions answered correctly by various students on a 1010-question quiz are an example of which type of data?
The numbers of questions answered correctly by various students on a 10 question quiz are an example of discrete data.
What is discrete data?Discrete data is the type of data that has clear spaces between values.
As a result, the test-scores are discrete data. Although most discrete data, refers to things we can count easily, it does not have to be numeric. Non-numeric categories could be described as discrete data.
Discrete data is a count that involves integers — only a limited number of values is possible. This type of data cannot be subdivided into different parts. Discrete data includes discrete variables that are finite, numeric, countable, and non-negative integers.
Discrete data is a type of quantitative data that includes figures and statistics of non divisible, single points of data that you can count. You typically write discrete data points as numbers that represent exact values, and discrete data usually represents single events that have already occurred. When reviewing discrete data, companies analyze exact figures like units that were sold on a given day or the hours that an employee worked during a certain week.
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